Ans: Given: Object distance u = -30 cm (negative, in front of mirror), Focal length f = -15 cm (concave mirror). Mirror formula: 1/v + 1/u = 1/f. 1/v = 1/f - 1/u = 1/(-15) - 1/(-30) = -1/15 + 1/30 = -2/30 + 1/30 = -1/30. Therefore v = -30 cm. Magnification m = -v/u = -(-30)/(-30) = -1. Image is: at 30 cm in front of mirror (real), inverted (m is negative), same size as object (|m| = 1), real image. This corresponds to the object being at C (centre of curvature) — image also forms at C, real and inverted, same size.

Ans: Total internal reflection (TIR) occurs when light traveling from a denser medium to a rarer medium hits the interface at an angle greater than the critical angle — all the light is reflected back into the denser medium, none is refracted. Conditions: (1) Light must travel from denser to rarer medium (e.g., glass to air, water to air). (2) The angle of incidence must be greater than the critical angle for that pair of media. Critical angle for glass-air ≈ 42°; for water-air ≈ 48°. Applications: optical fibres (data transmission — light signals travel long distances with no loss), diamonds sparkle (multiple TIR due to high refractive index), mirages (TIR in hot air near ground), endoscopes in medicine.

Ans: Convex lens (converging): thicker at center than edges. Light rays entering the lens refract toward the normal (denser medium), and due to the curved surfaces, all rays are bent toward the principal axis and converge at the focal point. Use: magnifying glass, correcting hypermetropia (farsightedness), cameras, microscopes. Concave lens (diverging): thinner at center than edges. Light rays entering refract, but the curvature bends them away from the principal axis, causing them to diverge as if coming from a virtual focal point on the same side as the object. Use: correcting myopia (nearsightedness), in combination with other lenses in telescopes and cameras.

Ans: P = 1/f = 1/0.20 = +5 D (convex lens).

Ans: Myopia (near-sightedness).

Ans: Virtual, erect, of the same size as the object, formed as far behind the mirror as the object is in front, and laterally inverted.

Ans: A convex mirror always gives an erect, diminished image and has a wider field of view, so the driver can see a larger area of traffic behind.

Ans: One dioptre is the power of a lens whose focal length is 1 metre.

Ans: Focal length f = R/2 = 32/2 = 16 cm (positive for a convex mirror).

Ans: There is no atmosphere in space to scatter sunlight, so no scattered blue light reaches the astronaut's eyes and the sky appears dark.

Ans: u = −20 cm, f = +10 cm. 1/v = 1/10 − 1/20 = 1/20, so v = +20 cm. m = v/u = 20/(−20) = −1. Image height = −5 cm. The image is at 20 cm on the other side, real, inverted and of the same size as the object.

Ans: A rainbow forms when sunlight passes through tiny water droplets in the air after rain. The droplets act like small prisms: light is refracted (and dispersed) on entering, internally reflected at the back of the droplet and refracted again on leaving. Different colours bend by different amounts, giving a spectrum in the sky. It is seen when the Sun is behind the observer and the water droplets are in front.

Ans: P = P₁ + P₂ = +2.5 + (−1.5) = +1.0 D. Focal length f = 1/P = 1/1 = 1 m = 100 cm. The combination behaves as a convex lens.

Ans: Dispersion is the splitting of white light into its constituent colours (VIBGYOR). When white light passes through a prism, each colour bends by a different angle: violet bends the most and red the least, since the refractive index of glass is different for different wavelengths. Newton placed a second inverted prism near the first; the colours recombined to give white light, showing that the prism does not add colours but only splits sunlight.

Ans: The cornea is the transparent front part where most refraction takes place; the iris controls the size of the pupil, which regulates the light entering; the eye lens focuses the image on the retina, which has light-sensitive cells that send signals through the optic nerve to the brain. Accommodation is the ability of the eye lens to change its focal length with the help of ciliary muscles to see both near and distant objects. The near point of a normal eye is about 25 cm; the far point is infinity.